Epidemic self-synchronization in complex networks of kuramoto oscillators

Advances in Complex Systems

Volumn 13, Issue 1, 2010, Pages 33-58

  Scholtes, Ingo ^a   Botev, Jean ^b   Esch, Markus ^b   Sturm, Peter ^a  

^a UNIVERSITY OF TRIER   (Germany)

^b UNIVERSITY OF LUXEMBOURG   (Luxembourg)

Author keywords

Complex communication networks; Kuramoto model; Nonlinear oscillators

Indexed keywords

EID: 77951678803     PISSN: 02195259     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219525910002426     Document Type: Article

References (35)

1. Acebrón, J. A., Bonilla, L. L., Vicente, C. J. P., Ritort, F. and Spigler, R., The kuramoto model: A simple paradigm for synchronization phenomena, Rev. Mod. Phys. 77 (2005) 137-185.
2. Babaoglu, O., Binci, T., Jelasity, M. and Montresor, A., Firefly-inspired heartbeat synchronization in overlay networks, in SASO '07: Proc. First Int. Conf. Self-Adaptive and Self-Organizing Systems (IEEE Computer Society, Washington, DC, USA, 2007), ISBN 0-7695-2906-2, pp. 77-86, DOI: 10.1142/S0219525910002426 http://dx.doi.org/10.1109/SASO.2007.25.
3. Barabasi, A.-L. and Albert, R., Emergence of scaling in random networks, Science 286 (1999) 509-512.
4. Barrat, A., Barthelemy, M. and Vespignani, A., Dynamical Processes on Compl ex Networks (Cambridge University Press, 2008).
5. Barrat, A. and Weigt, M., On the properties of small-world networks, Eur. Phys. J. B 13 (2000) 547-560.
6. di Bernardo, M., Garofalo, F. and Sorrentino, F., Synchronizability and synchronization dynamics of weighed and unweighed scale free networks with degree mixing (2005).
7. Ermentrout, B., Synchronization in a pool of mutually coupled oscillators with random frequencies, J. Math. Biol. 22 (1985) 1-9.
8. Ermentrout, B., An adaptive model for synchrony in the firefly pteroptyx malaccae, J. Math. Biol. 29 (1991) 571-585.
9. Ermentrout, G. B. and Kopell, N., Frequency plateaus in a chain of weakly coupled oscillators, i., SIAM J. Math. Anal. 15 (1984) 215-237.
10. Floyd, S., Floyd, S. and Jacobson, V., The synchronization of periodic routing messages, IEEE/ACM Trans. Netw. 2 (1994) 122-136.
11. Hwang, D.-U., Chavez, M., Amann, A. and Boccaletti, S., Synchronization in complex networks with age ordering, Phys. Rev. Lett. 94 (2005) 138701.
12. Ichinomiya, T., Frequency synchronization in a random oscillator network, Phys. Rev. E 70 (2004) 026116.
13. Izhikevich, E. M., Phase models with explicit time delays, Phys. Rev. E 58 (1998) 905-908.
14. Jelasity, M., Montresor, A. and Babaoglu, O., Gossip-based aggregation in large dynamic networks, ACM Trans. Comput. Syst. 23 (2005) 219-252.
15. Jelasity, M. and van Steen, M., Large-scale newscast computing on the Internet, Tech. Rep. IR-503, Vrije Universiteit Amsterdam, Department of Computer Science, Amsterdam, The Netherlands (2002), http://citeseer.ist.psu. edu/jelasity02 largescale.html.
16. Kac, M., Can one hear the shape of a drum?, Am. Math. Month. 73 (1966) 1-23.
17. Kuramoto, Y., Self-entrainment of a population of coupled nonlinear oscillators, in Int. Symp. Mathematical Problems in Theoretical Physics (Springer, 1975), pp. 420-422.
18. Li, X., Uniform synchronous criticality of diversely random complex networks, Phys. A Stat. Mech. Appl. 360 (2006) 629-636.
19. Li, X., The role of degree-weighted couplings in the synchronous onset of Kuramoto oscillator networks, Physica A: Stat. Mech. Appl. 387 (2008) 6624-6630.
20. Lucarelli, D. and Wang, I.-J., Decentralized synchronization protocols with nearest neighbor communication, in SenSys '04: Proc. 2nd Int. Conf. Embedded Networked Sensor Systems (ACM, New York, NY, USA, 2004), ISBN 1-58113-879-2, pp. 62-68, DOI: 10.1142/S0219525910002426 http://doi.acm.org/10. 1145/1031495.1031503.
21. Mirollo, R. E. and Strogatz, S. H., Synchronization of pulse-coupled biological oscillators, SIAM J. Appl. Math. 50 (1990) 1645-1662.
22. Moreno, Y. and Pacheco, A. F., Synchronization of Kuramoto oscillators in scale-free networks, Europhys. Lett. 68 (2004) 603-609.
23. Motter, A. E., Zhou, C. and Kurths, J., Network synchronization, diffusion, and the paradox of heterogeneity, Phys. Rev. E (Stat. Nonlinear Soft Matter Phys.) 71 (2005) 016116.
24. Peskin, C. S., Mathematical aspects of heart physiology, Technical report, Courant Institute of Mathematical Sciences (1975), http://www.math.nyu. edu/faculty/peskin/heartnotes/index.html.
25. Ripeanu, M. and Foster, I., Mapping the gnutella network: Macroscopic properties of large-scale peer-to-peer systems (2002).
26. R Development Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria (2009), http://www. R-project.org, ISBN 3-900051-07-0.
27. Scholtes, I., Botev, J., Esch, M., Hoehfeld, A., Schloss, H. and Zech, B., Topgen - internet router-level topology generation based on technology constraints, in Proc. First Int. Conf. on Simulation Tools and Techniques for Communications, Networks and Systems (SIMUTools) (2008).
28. Scholtes, I., Botev, J., Esch, M., and Sturm, P., Epidemic self-synchronization in complex networks, in Proc. 1st Int. Conf. on Complex Sciences: Theory and Applications (2009).
29. Strogatz, S. H. and Mirollo, R. E., Phase-locking and critical phenomena in lattices of coupled nonlinear oscillators with random intrinsic frequencies, Phys. D 31 (1988) 143-168.
30. Strogatz, S. H., From Kuramoto to crawford: exploring the onset of synchronization in populations of coupled oscillators, Phys. D 143 (2000) 1-20.
31. Strogatz, S. H., Sync: The Emerging Science of Spontaneous Order (Hyperion, 2003).
32. Watts, D. J. and Strogatz, S. H., Collective dynamics of 'small-world' networks, Nature 393 (1998).
33. Watts, D. J., Small Worlds: The Dynamics of Networks between Order and Randomness (Princeton University Press, 1999).
34. Wiener, N., Nonlinear Problems in Random Theory (MIT Press, 1958).
35. Winfree, A. T., Biological rhythms and the behavior of populations of coupled oscillators, J. Theor. Biol. 16 (1967) 15-42.